Finite Group Databasebeta

C8×#6505 #13323221

order1792
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productC8×#6505

Splittings

FittingC2×C7×C8×Q8 ⋊ C2
SylowC7 ⋊ C8×#137

Subgroups

subgroupG/H
centerC2×C8C2×C22⋊D7
commutatorC4×C7C23×C8
FrattiniC42C23×D7
FittingC2×C7×C8×Q8C2
socleC22×C7C2×C4×D4
prime radicalC2×#1157C2×C4
cosocleC42×C7C24
hypercenterC2×C8×Q8D7
hypocenterC7C8×#137
LCSG ▷ C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C8 ◁ C2×C4×C8 ◁ C2×C8×Q8

714 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 896

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 138993);