Finite Group Databasebeta

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C2×#19135531 #25101038

order11008
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×#19135531

Splittings

SylowC43 ⋊ C2×#1984

Subgroups

subgroupG/H
centerC23×C4C22×D43
commutatorC22×C43C23×C8
FrattiniC22×C4C23×D43
FittingC22×C4×C8×C43C2
socle, prime radicalC24×C43C22×C4
cosocleC22×C4×C43C24
hypercenterC22×C4×C8D43
hypocenterC43C2×#1984
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23×C4 ◁ C22×C4×C8

1502 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2800 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 174009);