Finite Group Databasebeta

C2×Dic592 #17996901

order4736
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×Dic592

Splittings

SylowC37 ⋊ C2×Q64

Subgroups

subgroupG/H
centerC22D592
commutator, cosocleC16×C37C23
FrattiniC16C22×D37
FittingC2×C32×C37C2
socle, prime radicalC22×C37D16
hypercenterC2×C32D37
hypocenterC37C2×Q64
LCSG ▷ C16×C37 ▷ C8×C37 ▷ C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ C2×C32

104 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4736

Conjugacy classes & character table

1190 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 6815);