Finite Group Databasebeta

C2×#19132549 #25006295

order11008
automorphism?
homologyAbelianization (H1) = C22×C16 · Schur multiplier (H2) = C24

Aliases

direct productC2×#19132549

Splittings

FittingC2×C43×C4⋊C16 ⋊ C2
SylowC43 ⋊ C2×D4⋊C16

Subgroups

subgroupG/H
centerC22×C8C22⋊D43
commutatorC4×C43C22×C16
FrattiniC4×C8C22×D43
FittingC2×C43×C4⋊C16C2
socleC23×C43C22⋊C8
prime radicalC22×D172C8
cosocleC4×C8×C43C23
hypercenterC2×C4⋊C16D43
hypocenterC43C2×D4⋊C16
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C8 ◁ C2×C4×C8 ◁ C2×C4⋊C16

470 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, 79266);