Finite Group Databasebeta

C2×#28414576 #44444772

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

Aliases

direct productC2×#28414576

Splittings

SylowC463 ⋊ C2×#101

Subgroups

subgroupG/H
centerC22(C2×D463)⋊C4
commutatorC22×C463C22×C4
FrattiniC2×C4C22×D463
FittingC2×M16×C463C2
socleC22×C463C22⋊C4
prime radicalC23×C463C2×C4
cosocleC2×C4×C463C23
hypercenterC2×M16D463
hypocenterC463C2×#101
LCSG ▷ C22×C463 ▷ C2×C463 ▷ C463
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

146 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14816

Conjugacy classes & character table

4642 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29632, 528);