Finite Group Databasebeta

C4×Dic232 #16821352

order3712
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct productC4×Dic232

Splittings

SylowC29 ⋊ C4×Q32

Subgroups

subgroupG/H
centerC2×C4D232
commutatorC8×C29C22×C4
FrattiniC2×C8C22×D29
FittingC4×C16×C29C2
socle, prime radicalC22×C29C2×D8
cosocleC2×C8×C29C23
hypercenterC4×C16D29
hypocenterC29C4×Q32
LCSG ▷ C8×C29 ▷ C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8 ◁ C4×C16

150 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3712

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 6370);