Finite Group Databasebeta

C2×C8×#11757210 #29508671

order15424
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4

Aliases

direct productC2×C8×#11757210

Splittings

FittingC2×C8×C241 ⋊ C4
derived, SylowC241 ⋊ C2×C4×C8

Subgroups

subgroupG/H
center, hypercenterC2×C8#11757210
commutator, hypocenterC241C2×C4×C8
FrattiniC4C22×#11757210
FittingC2×C8×C241C4
socleC22×C241C42
prime radicalC22×D241C2×C4
cosocleC4×D241C23
LCSG ▷ C241
UCSC1 ◁ C2×C8

162 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3856

Conjugacy classes & character table

1024 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15424, 1503);