C₂³×C₄×Dic₁₀₁ #27184287

order	12928
isoclinism	isoclinic class of D₁₀₁
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄² · Schur multiplier (H₂) = C₂⁹×C₄

Aliases

direct product

C₂³×C₄×Dic₁₀₁

Splittings

derived, Sylow

C₁₀₁ ⋊ C₂³×C₄²

Subgroups

	subgroup	G/H
center, hypercenter	C₂⁴×C₄	D₁₀₁
commutator, hypocenter	C₁₀₁	C₂³×C₄²
Frattini	C₂²	C₂⁴×D₁₀₁
Fitting	C₂⁴×C₄×C₁₀₁	C₂
socle, prime radical	C₂⁵×C₁₀₁	C₂²
cosocle	C₂²×C₁₀₁	C₂⁵
LCS	G ▷ C₁₀₁
UCS	C₁ ◁ C₂⁴×C₄

3000 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 115
transitive degree	μ_t(G) = 12928

A minimal faithful permutation representation — 5 generators on 115 points:

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

Conjugacy classes & character table

3328 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12928, 17665);

C23×C4×Dic101 #27184287