Finite Group Databasebeta

C8×#10597279 #18073832

order4864
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C2×C4

Aliases

direct productC8×#10597279

Splittings

SylowC19 ⋊ C8×#108

Subgroups

subgroupG/H
centerC4×C8C22⋊D19
commutatorC4×C19C2×C4×C8
FrattiniC2×C42C22×D19
FittingC8×M16×C19C2
socleC22×C19C4×C4⋊C4
prime radicalC23×C19C4×Q8
cosocleC2×C42×C19C23
hypercenterC8×M16D19
hypocenterC19C8×#108
LCSG ▷ C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C4×C8 ◁ C2×C4×C8 ◁ C8×M16

374 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2432

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 60861);