Finite Group Databasebeta

C2×#28414577 #44444773

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

Aliases

direct productC2×#28414577

Splittings

SylowC463 ⋊ C2×#101

Subgroups

subgroupG/H
centerC22C22⋊Dic463
commutatorC22×C463C22×C4
FrattiniC2×C4C22×D463
FittingC22×Q8×C463C2
socleC22×C463C22⋊C4
prime radicalC23×C463C2×C4
cosocleC2×C4×C463C23
hypercenterC22×Q8D463
hypocenterC463C2×#101
LCSG ▷ C22×C463 ▷ C2×C463 ▷ C463
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

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, 529);