Finite Group Databasebeta

C2×#11929611 #14579174

order2528
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×#11929611

Splittings

FittingC2×Q8×C79 ⋊ C2
SylowC79 ⋊ C2×SD16

Subgroups

subgroupG/H
centerC22C22⋊D79
commutator, cosocleC4×C79C23
FrattiniC4C22×D79
FittingC2×Q8×C79C2
socleC22×C79D4
prime radicalC2×D316C2
hypercenterC2×Q8D79
hypocenterC79C2×SD16
LCSG ▷ C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q8

68 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1264

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2528, 159);