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#44449694

order	29824
automorphism	?
homology	Abelianization (H₁) = C₄² · Schur multiplier (H₂) = C₂³

Aliases

No aliases for this group.

Splittings

C₂₃₃ ⋊ #1296

Subgroups

	subgroup	G/H
center	C₂³	#16836571
commutator	C₂×C₄×C₂₃₃	C₄²
Frattini	C₂×C₄²	C₂×D₂₃₃
Fitting	C₂×C₄⋊C₈×C₂₃₃	C₂
socle, prime radical	C₂³×C₂₃₃	C₂²⋊C₄
cosocle	C₂×C₄²×C₂₃₃	C₂²
hypercenter	C₂×C₄⋊C₈	D₂₃₃
hypocenter	C₂₃₃	#1296
LCS	G ▷ C₂×C₄×C₂₃₃ ▷ C₂²×C₂₃₃ ▷ C₂₃₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄⋊C₈

188 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 29824

Polycyclic presentation:

2^7,233|a^2=d,b^2=e,c^2=f,e^2=fg,b^a=bc,c^a=cf,e^a=efg,h^a=h^232,c^b=cg

Conjugacy classes & character table

4678 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29824, 2394);