Finite Group Databasebeta

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C2×#19135319 #25099869

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

Aliases

direct productC2×#19135319

Splittings

SylowC43 ⋊ C2×#1940

Subgroups

subgroupG/H
centerC23×C4C22×D43
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C4×C4⋊C4×C43C2
socle, prime radicalC24×C43C22×C4
cosocleC22×C4×C43C24
hypercenterC2×C4×C4⋊C4D43
hypocenterC43C2×#1940
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23×C4 ◁ C2×C4×C4⋊C4

1182 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1768 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 172840);