Finite Group Databasebeta

C2×#27131637 #37566914

order24352
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×#27131637

Splittings

SylowC761 ⋊ C2×SD16

Subgroups

subgroupG/H
centerC22C22⋊D761
commutator, cosocleC4×C761C23
FrattiniC4C22×D761
Fitting, prime radicalC2×D4×C761C2
socleC22×C761D4
hypercenterC2×D4D761
hypocenterC761C2×SD16
LCSG ▷ C4×C761 ▷ C2×C761 ▷ C761
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D4

68 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12176

Conjugacy classes & character table

3814 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24352, 160);