Finite Group Databasebeta

C2×#28414172 #44443033

order29504
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C23

Aliases

direct productC2×#28414172

Splittings

FittingC2×C8×C461 ⋊ C4
SylowC461 ⋊ C2×#97

Subgroups

subgroupG/H
centerC2×C4C2×#14270406
commutatorC2×C461C2×C42
FrattiniC4C22×#14270406
FittingC2×C8×C461C4
socleC22×C461C42
prime radicalC22×D461C2×C4
cosocleC4×D461C23
hypercenterC2×C8#14270406
hypocenterC461C2×#97
LCSG ▷ C2×C461 ▷ C461
UCSC1 ◁ C2×C4 ◁ C2×C8

146 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7376

Conjugacy classes & character table

1880 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29504, 1506);