C₃²×Dic₂₈ #11759243

order	1008
isoclinism	isoclinic class of #1132
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃² · Schur multiplier (H₂) = C₃

Aliases

direct product

C₃²×Dic₂₈

Splittings

Hall	C₃²×C₇ ⋊ Q₁₆
Sylow	C₇ ⋊ C₃²×Q₁₆

Subgroups

	subgroup	G/H
center	C₂×C₃²	D₂₈
commutator, cosocle	C₄×C₇	C₂²×C₃²
Frattini	C₄	C₂×C₃²×D₇
Fitting	C₃²×C₇×C₈	C₂
socle, prime radical	C₂×C₃²×C₇	D₄
hypercenter	C₃²×C₈	D₇
hypocenter	C₇	C₃²×Q₁₆
LCS	G ▷ C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂×C₃² ◁ C₃²×C₄ ◁ C₃²×C₈

108 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 29
transitive degree	μ_t(G) = 1008

A minimal faithful permutation representation — 2 generators on 29 points:

(1,2,3)(7,8,9,10,11,12,13,14)(15,22,21,20,19,18,17,16)(23,24,25,26,27,28,29);(4,5,6)(7,15,11,19)(8,16,12,20)(9,17,13,21)(10,18,14,22)(24,29)(25,28)(26,27)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1008, 414);

C32×Dic28 #11759243