Finite Group Databasebeta

C2×#27131639 #37566917

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

Aliases

direct productC2×#27131639

Splittings

SylowC761 ⋊ C2×Q16

Subgroups

subgroupG/H
centerC22C22⋊D761
commutator, cosocleC4×C761C23
FrattiniC4C22×D761
FittingC2×Q8×C761C2
socle, prime radicalC22×C761D4
hypercenterC2×Q8D761
hypocenterC761C2×Q16
LCSG ▷ C4×C761 ▷ C2×C761 ▷ C761
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q8

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 24352

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, 163);