Finite Group Databasebeta

C2×C8×#13097544 #38763476

order25408
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4

Aliases

direct productC2×C8×#13097544

Splittings

FittingC2×C8×C397 ⋊ C4
derived, SylowC397 ⋊ C2×C4×C8

Subgroups

subgroupG/H
center, hypercenterC2×C8#13097544
commutator, hypocenterC397C2×C4×C8
FrattiniC4C22×#13097544
FittingC2×C8×C397C4
socleC22×C397C42
prime radicalC22×D397C2×C4
cosocleC4×D397C23
LCSG ▷ C397
UCSC1 ◁ C2×C8

162 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6352

Conjugacy classes & character table

1648 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25408, 1503);