Finite Group Databasebeta

C2×#23755626 #34091673

order19904
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×#23755626

Splittings

SylowC311 ⋊ C2×#101

Subgroups

subgroupG/H
centerC22(C2×D311)⋊C4
commutatorC22×C311C22×C4
FrattiniC2×C4C22×D311
FittingC2×M16×C311C2
socleC22×C311C22⋊C4
prime radicalC23×C311C2×C4
cosocleC2×C4×C311C23
hypercenterC2×M16D311
hypocenterC311C2×#101
LCSG ▷ C22×C311 ▷ C2×C311 ▷ C311
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

146 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9952

Conjugacy classes & character table

3122 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19904, 528);