Finite Group Databasebeta

C2×#22580793 #31808708

order17792
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×#22580793

Splittings

SylowC139 ⋊ C2×Q64

Subgroups

subgroupG/H
centerC22#17984783
commutator, cosocleC16×C139C23
FrattiniC16C22×D139
FittingC2×Q32×C139C2
socle, prime radicalC22×C139D16
hypercenterC2×Q32D139
hypocenterC139C2×Q64
LCSG ▷ C16×C139 ▷ C8×C139 ▷ C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ C2×Q32

104 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17792

Conjugacy classes & character table

1556 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17792, 6814);