Finite Group Databasebeta

C2×#19132554 #25006313

order11008
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C23

Aliases

direct productC2×#19132554

Splittings

FittingC2×C43×#346 ⋊ C2
SylowC43 ⋊ C2×#1330

Subgroups

subgroupG/H
centerC22×C4(C2×D43)⋊C4
commutatorC2×C4×C43C22×C8
FrattiniC4×C8C22×D43
FittingC2×C43×#346C2
socleC23×C43C22⋊C8
prime radicalC22×D172C8
cosocleC4×C8×C43C23
hypercenterC2×#346D43
hypocenterC43C2×#1330
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C2×C4×C8 ◁ C2×#346

422 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, 79284);