Finite Group Databasebeta

C2×#28414592 #44444827

order29632
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×#28414592

Splittings

SylowC463 ⋊ C2×#107

Subgroups

subgroupG/H
centerC23D1852
commutatorC4×C463C22×C4
FrattiniC2×C4C22×D463
FittingC22×C8×C463C2
socle, prime radicalC23×C463D4
cosocleC2×C4×C463C23
hypercenterC22×C8D463
hypocenterC463C2×#107
LCSG ▷ C4×C463 ▷ C2×C463 ▷ C463
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

130 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 29632

Conjugacy classes & character table

7420 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29632, 583);