Finite Group Databasebeta

C2×Q8×D79 #14579200

order2528
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC2×Q8×D79

Splittings

FittingC2×Q8×C79 ⋊ C2
SylowC79 ⋊ C22×Q8

Subgroups

subgroupG/H
centerC22C22×D79
commutator, cosocleC2×C79C24
FrattiniC2C23×D79
FittingC2×Q8×C79C2
socleC22×C79C23
prime radicalC22×D79C22
hypercenterC2×Q8D79
hypocenterC79C22×Q8
LCSG ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C2×Q8

156 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1264

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2528, 185);