Finite Group Databasebeta

C2×Dic568 #17986427

order4544
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×Dic568

Splittings

SylowC71 ⋊ C2×Q32

Subgroups

subgroupG/H
centerC22D568
commutator, cosocleC8×C71C23
FrattiniC8C22×D71
FittingC2×C16×C71C2
socle, prime radicalC22×C71D8
hypercenterC2×C16D71
hypocenterC71C2×Q32
LCSG ▷ C8×C71 ▷ C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16

82 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4544

Conjugacy classes & character table

1142 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4544, 977);