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#44482423

order	30592
automorphism	?
homology	Abelianization (H₁) = C₄² · Schur multiplier (H₂) = C₂²

Aliases

No aliases for this group.

Splittings

C₂₃₉ ⋊ #1292

Subgroups

	subgroup	G/H
center	C₂²	C₂₃₉⋊#95
commutator	C₂×C₄×C₂₃₉	C₄²
Frattini	C₂×C₄²	C₂×D₂₃₉
Fitting	C₂×C₄⋊C₈×C₂₃₉	C₂
socle	C₂²×C₂₃₉	#95
prime radical	C₂³×C₂₃₉	C₄⋊C₄
cosocle	C₂×C₄²×C₂₃₉	C₂²
hypercenter	C₂×C₄⋊C₈	D₂₃₉
hypocenter	C₂₃₉	#1292
LCS	G ▷ C₂×C₄×C₂₃₉ ▷ C₂×C₂₃₉ ▷ C₂₃₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄⋊C₈

152 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 15296

Polycyclic presentation:

2^7,239|a^2=d,b^2=e,c^2=fg,d^2=g,e^2=fg,b^a=bc,c^a=cf,e^a=efg,h^a=h^238,d^b=dg

Conjugacy classes & character table

4792 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30592, 2385);