Finite Group Databasebeta

C23×#90779 #16832652

order3712
isoclinismisoclinic class of Dic58
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC23×#90779

Splittings

SylowC29 ⋊ C23×C4⋊C4

Subgroups

subgroupG/H
centerC25C2×D29
commutatorC2×C29C24×C4
FrattiniC22C24×D29
FittingC24×C4×C29C2
socle, prime radicalC25×C29C22
cosocleC22×C29C25
hypercenterC24×C4D29
hypocenterC29C23×C4⋊C4
LCSG ▷ C2×C29 ▷ C29
UCSC1 ◁ C25 ◁ C24×C4

2488 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3712

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 17670);