Finite Group Databasebeta

C2×Dic344 #14583327

order2752
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×Dic344

Splittings

SylowC43 ⋊ C2×Q32

Subgroups

subgroupG/H
centerC22D344
commutator, cosocleC8×C43C23
FrattiniC8C22×D43
FittingC2×C16×C43C2
socle, prime radicalC22×C43D8
hypercenterC2×C16D43
hypocenterC43C2×Q32
LCSG ▷ C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16

82 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2752

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2752, 977);