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#49093187

order	35968
automorphism	?
homology	Abelianization (H₁) = C₄² · Schur multiplier (H₂) = C₂³

Aliases

No aliases for this group.

Splittings

C₂₈₁ ⋊ #1296

Subgroups

	subgroup	G/H
center	C₂³	#17985115
commutator	C₂×C₄×C₂₈₁	C₄²
Frattini	C₂×C₄²	C₂×D₂₈₁
Fitting	C₂×C₄⋊C₈×C₂₈₁	C₂
socle, prime radical	C₂³×C₂₈₁	C₂²⋊C₄
cosocle	C₂×C₄²×C₂₈₁	C₂²
hypercenter	C₂×C₄⋊C₈	D₂₈₁
hypocenter	C₂₈₁	#1296
LCS	G ▷ C₂×C₄×C₂₈₁ ▷ C₂²×C₂₈₁ ▷ C₂₈₁
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄⋊C₈

188 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 35968

Polycyclic presentation:

2^7,281|a^2=d,b^2=e,c^2=f,e^2=fg,b^a=bc,c^a=cf,e^a=efg,h^a=h^280,c^b=cg

Conjugacy classes & character table

5638 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35968, 2394);