Finite Group Databasebeta

C22×#11745166 #16828067

order3712
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC22×#11745166

Splittings

SylowC29 ⋊ C22×#107

Subgroups

subgroupG/H
centerC24D116
commutatorC4×C29C23×C4
FrattiniC2×C4C23×D29
FittingC23×C8×C29C2
socle, prime radicalC24×C29D4
cosocleC2×C4×C29C24
hypercenterC23×C8D29
hypocenterC29C22×#107
LCSG ▷ C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C24 ◁ C23×C4 ◁ C23×C8

600 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3712

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 13085);