Finite Group Databasebeta

C2×#23755654 #34092121

order19904
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×#23755654

Splittings

SylowC311 ⋊ C2×Q32

Subgroups

subgroupG/H
centerC22#19097300
commutator, cosocleC8×C311C23
FrattiniC8C22×D311
FittingC2×Q16×C311C2
socle, prime radicalC22×C311D8
hypercenterC2×Q16D311
hypocenterC311C2×Q32
LCSG ▷ C8×C311 ▷ C4×C311 ▷ C2×C311 ▷ C311
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q16

82 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 19904

Conjugacy classes & character table

2192 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19904, 976);