Finite Group Databasebeta

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C2×#19139208 #25265912

order11008
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C27

Aliases

direct productC2×#19139208

Splittings

FittingC2×C4×C4⋊C4×C43 ⋊ C2
SylowC43 ⋊ C2×#2515

Subgroups

subgroupG/H
centerC24C23×D43
commutator, cosocleC23×C43C25
FrattiniC23C24×D43
FittingC2×C4×C4⋊C4×C43C2
socleC24×C43C24
prime radicalC24×D43C23
hypercenterC2×C4×C4⋊C4D43
hypocenterC43C2×#2515
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

2182 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1756 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 338883);