Finite Group Databasebeta

C2×C4×#15691794 #38763477

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

Aliases

direct productC2×C4×#15691794

Splittings

derived, SylowC397 ⋊ C2×C4×C8

Subgroups

subgroupG/H
center, hypercenterC22×C4#13097544
commutator, hypocenterC397C2×C4×C8
FrattiniC22C22×#13097544
FittingC22×C4×C397C4
socle, prime radicalC23×C397C2×C4
cosocleC2×Dic397C23
LCSG ▷ C397
UCSC1 ◁ C22×C4

162 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 25408

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, 1504);