Finite Group Databasebeta

C2×C8×#13109888 #39910201

order26176
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4

Aliases

direct productC2×C8×#13109888

Splittings

FittingC2×C8×C409 ⋊ C4
derived, SylowC409 ⋊ C2×C4×C8

Subgroups

subgroupG/H
center, hypercenterC2×C8#13109888
commutator, hypocenterC409C2×C4×C8
FrattiniC4C22×#13109888
FittingC2×C8×C409C4
socleC22×C409C42
prime radicalC22×D409C2×C4
cosocleC4×D409C23
LCSG ▷ C409
UCSC1 ◁ C2×C8

162 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6544

Conjugacy classes & character table

1696 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26176, 1503);