Finite Group Databasebeta

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C2×#19132443 #24986246

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

Aliases

direct productC2×#19132443

Splittings

SylowC43 ⋊ C2×#1282

Subgroups

subgroupG/H
centerC22×C4(C2×D43)⋊C4
commutatorC22×C43C2×C4×C8
FrattiniC23×C4C22×D43
FittingC2×C4×C22⋊C4×C43C2
socleC23×C43#95
prime radicalC25×C43C2×C4
cosocleC23×C4×C43C23
hypercenterC2×C4×C22⋊C4D43
hypocenterC43C2×#1282
LCSG ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C24×C4 ◁ C2×C4×C22⋊C4

1130 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, 59217);