Finite Group Databasebeta

C2×C8×#14523438 #45688386

order33344
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4

Aliases

direct productC2×C8×#14523438

Splittings

FittingC2×C8×C521 ⋊ C4
derived, SylowC521 ⋊ C2×C4×C8

Subgroups

subgroupG/H
center, hypercenterC2×C8#14523438
commutator, hypocenterC521C2×C4×C8
FrattiniC4C22×#14523438
FittingC2×C8×C521C4
socleC22×C521C42
prime radicalC22×D521C2×C4
cosocleC4×D521C23
LCSG ▷ C521
UCSC1 ◁ C2×C8

162 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8336

Conjugacy classes & character table

2144 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33344, 1503);