Finite Group Databasebeta

C2×#19132489 #24986790

order11008
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4

Aliases

direct productC2×#19132489

Splittings

SylowC43 ⋊ C2×#1300

Subgroups

subgroupG/H
centerC22×C4(C2×D43)⋊C4
commutatorC2×C4×C43C2×C42
FrattiniC2×C42C22×D43
FittingC2×C4×M16×C43C2
socleC23×C43#95
prime radicalC24×C43C22⋊C4
cosocleC2×C42×C43C23
hypercenterC2×C4×M16D43
hypocenterC43C2×#1300
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C2×C4×M16

786 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, 59761);