Finite Group Databasebeta

C2×#28414028 #44442024

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

Aliases

direct productC2×#28414028

Splittings

SylowC461 ⋊ C2×#97

Subgroups

subgroupG/H
centerC22×C4C2×D461
commutatorC2×C461C2×C42
FrattiniC2×C4C22×D461
FittingC22×C8×C461C2
socle, prime radicalC23×C461C2×C4
cosocleC2×C4×C461C23
hypercenterC22×C8D461
hypocenterC461C2×#97
LCSG ▷ C2×C461 ▷ C461
UCSC1 ◁ C22×C4 ◁ C22×C8

146 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 29504

Conjugacy classes & character table

7400 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29504, 497);