Finite Group Databasebeta

C22×#11745151 #16827896

order3712
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C26

Aliases

direct productC22×#11745151

Splittings

SylowC29 ⋊ C22×#97

Subgroups

subgroupG/H
centerC23×C4C2×D29
commutatorC2×C29C22×C42
FrattiniC2×C4C23×D29
FittingC22×C42×C29C2
socle, prime radicalC24×C29C2×C4
cosocleC2×C4×C29C24
hypercenterC22×C42D29
hypocenterC29C22×#97
LCSG ▷ C2×C29 ▷ C29
UCSC1 ◁ C23×C4 ◁ C22×C42

680 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, 12914);