Finite Group Databasebeta

C2×#28414594 #44444839

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

Aliases

direct productC2×#28414594

Splittings

SylowC463 ⋊ C2×#108

Subgroups

subgroupG/H
centerC2×C4D1852
commutatorC4×C463C22×C4
FrattiniC2×C4C22×D463
FittingC22×C8×C463C2
socleC22×C463C4⋊C4
prime radicalC23×C463Q8
cosocleC2×C4×C463C23
hypercenterC22×C8D463
hypocenterC463C2×#108
LCSG ▷ C4×C463 ▷ C2×C463 ▷ C463
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8

106 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14816

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, 595);