C₃×#87707 #11924792

order	1200
isoclinism	isoclinic class of D₂₅
automorphism	?
homology	Abelianization (H₁) = C₃×C₁₆ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₃×#87707

Splittings

derived, Sylow	C₂₅ ⋊ C₃×C₁₆
Hall	C₃×C₂₅ ⋊ C₁₆

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₈	D₂₅
commutator, hypocenter	C₂₅	C₃×C₁₆
Frattini	C₅×C₈	C₃×D₅
Fitting	C₃×C₈×C₂₅	C₂
socle, prime radical	C₂×C₃×C₅	#168
cosocle	C₈×C₂₅	C₂×C₃
LCS	G ▷ C₂₅
UCS	C₁ ◁ C₃×C₈

30 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 44
transitive degree	μ_t(G) = 1200

A minimal faithful permutation representation — 2 generators on 44 points:

(1,2,3)(5,7)(6,10)(8,13)(9,16)(11,19)(12,18)(14,15)(17,23)(20,24)(21,25)(22,27)(26,28)(29,30,31,34,32,35,37,40,33,36,38,41,39,42,43,44);(4,18,28,21,7,10,24,22,13,16,19,17,15,14,23,11,9,8,27,20,6,5,25,26,12)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1200, 2);

C3×#87707 #11924792