Finite Group Databasebeta

C2×#11929608 #14579166

order2528
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct productC2×#11929608

Splittings

SylowC79 ⋊ C2×M16

Subgroups

subgroupG/H
centerC2×C4C2×D79
commutatorC2×C79C22×C4
FrattiniC4C22×D79
FittingC22×C4×C79C2
socleC22×C79C2×C4
prime radicalC23×C79C4
cosocleC4×C79C23
hypercenterC22×C4D79
hypocenterC79C2×M16
LCSG ▷ C2×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ C22×C4

68 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1264

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2528, 151);