Finite Group Databasebeta

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C2×#19132436 #24986122

order11008
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C25

Aliases

direct productC2×#19132436

Splittings

SylowC43 ⋊ C2×#1279

Subgroups

subgroupG/H
centerC23×C4C22⋊D43
commutatorC4×C43C2×C4×C8
FrattiniC2×C42C22×D43
FittingC2×C4×C4⋊C4×C43C2
socle, prime radicalC24×C43C22⋊C4
cosocleC2×C42×C43C23
hypercenterC2×C4×C4⋊C4D43
hypocenterC43C2×#1279
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23×C4 ◁ C22×C42 ◁ C2×C4×C4⋊C4

974 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1792 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 59093);