C₂⁵×#89137 #28380029

order	13952
isoclinism	isoclinic class of #89137
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₄ · Schur multiplier (H₂) = C₂¹⁵

Aliases

direct product	C₂⁵×#89137
unambiguous semidirect product	D₁₀₉⋊(C₂⁴×C₄)

Splittings

Fitting, socle	C₂⁵×C₁₀₉ ⋊ C₄
derived, Sylow	C₁₀₉ ⋊ C₂⁵×C₄

Subgroups

	subgroup	G/H
center, hypercenter	C₂⁵	#89137
commutator, hypocenter	C₁₀₉	C₂⁵×C₄
Frattini	C₁	G
Fitting, socle	C₂⁵×C₁₀₉	C₄
prime radical	C₂⁵×D₁₀₉	C₂
cosocle	D₁₀₉	C₂⁶
LCS	G ▷ C₁₀₉
UCS	C₁ ◁ C₂⁵

10552 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 119
transitive degree	μ_t(G) = 3488

A minimal faithful permutation representation — 6 generators on 119 points:

(12,13,14,16)(15,18,19,25)(17,22,23,21)(20,27,28,38)(24,31,32,34)(26,35,36,30)(29,40,41,55)(33,44,45,51)(37,48,49,47)(39,52,53,43)(42,57,58,76)(46,61,62,72)(50,65,66,68)(54,69,70,64)(56,73,74,60)(59,78,79,97)(63,82,83,93)(67,86,84,89)(71,88,80,87)(75,90,91,85)(77,94,95,81)(92,102,103,101)(96,105,106,100)(98,104,108,99)(107,112,113,111)(109,114,115,110)(116,118,119,117);(9,10)(11,12,15,20,29,42,59,80,70,53,38,51,68,87,101,111,117,119,115,108,97,86,61,40,56,75,92,104,94,73,52,35,22,13,17,24,33,46,63,84,66,49,36,25,34,47,64,85,100,110,113,106,95,76,93,82,57,77,96,107,114,105,90,69,48,31,18,26,37,50,67,83,62,45,32,23,16,21,30,43,60,81,99,103,91,74,55,72,89,78,98,109,116,118,112,102,88,65,44,27,39,54,71,79,58,41,28,19,14);(7,8);(5,6);(3,4);(1,2)

Conjugacy classes & character table

992 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 21507);

C25×#89137 #28380029