Finite Group Databasebeta

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#108×C₄₇⋊C₈ #26107572

order	12032
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₈ · Schur multiplier (H₂) = C₂×C₄

Aliases

#108×C₄₇⋊C₈

Splittings

C₄₇ ⋊ C₈×#108

Subgroups

	subgroup	G/H
center	C₄²	D₄×D₄₇
commutator	C₄×C₄₇	C₂×C₄×C₈
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₄×#108×C₄₇	C₂
socle	C₂²×C₄₇	C₄×C₄⋊C₄
prime radical	C₂³×C₄₇	C₄×Q₈
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	C₄×#108	D₄₇
hypocenter	C₄₇	C₈×#108
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₄² ◁ C₂×C₄² ◁ C₄×#108

374 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1400 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 60862);