Finite Group Databasebeta

C2×Dic544 #16955374

order4352
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×Dic544

Splittings

SylowC17 ⋊ C2×Q128

Subgroups

subgroupG/H
centerC22D544
commutator, cosocleC17×C32C23
FrattiniC32C22×D17
FittingC2×C17×C64C2
socle, prime radicalC22×C17D32
hypercenterC2×C64D17
hypocenterC17C2×Q128
LCSG ▷ C17×C32 ▷ C16×C17 ▷ C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ C2×C32 ◁ C2×C64

126 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4352

Conjugacy classes & character table

1094 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 90618);