Finite Group Databasebeta

C2×C8×#13132997 #41003794

order26944
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4

Aliases

direct productC2×C8×#13132997

Splittings

FittingC2×C8×C421 ⋊ C4
derived, SylowC421 ⋊ C2×C4×C8

Subgroups

subgroupG/H
center, hypercenterC2×C8#13132997
commutator, hypocenterC421C2×C4×C8
FrattiniC4C22×#13132997
FittingC2×C8×C421C4
socleC22×C421C42
prime radicalC22×D421C2×C4
cosocleC4×D421C23
LCSG ▷ C421
UCSC1 ◁ C2×C8

162 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6736

Conjugacy classes & character table

1744 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26944, 1503);