Finite Group Databasebeta

C2×C8×#14270406 #44443030

order29504
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4

Aliases

direct productC2×C8×#14270406

Splittings

FittingC2×C8×C461 ⋊ C4
derived, SylowC461 ⋊ C2×C4×C8

Subgroups

subgroupG/H
center, hypercenterC2×C8#14270406
commutator, hypocenterC461C2×C4×C8
FrattiniC4C22×#14270406
FittingC2×C8×C461C4
socleC22×C461C42
prime radicalC22×D461C2×C4
cosocleC4×D461C23
LCSG ▷ C461
UCSC1 ◁ C2×C8

162 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7376

Conjugacy classes & character table

1904 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29504, 1503);