Finite Group Databasebeta

C2×#26046630 #37562452

order24032
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×#26046630

Splittings

SylowC751 ⋊ C2×SD16

Subgroups

subgroupG/H
centerC22C22⋊D751
commutator, cosocleC4×C751C23
FrattiniC4C22×D751
Fitting, prime radicalC2×D4×C751C2
socleC22×C751D4
hypercenterC2×D4D751
hypocenterC751C2×SD16
LCSG ▷ C4×C751 ▷ C2×C751 ▷ C751
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D4

68 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12016

Conjugacy classes & character table

3764 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24032, 160);