Finite Group Databasebeta

← Prev (#34022132) Next (#34022134) →

C2×#22626044 #34022133

order18688
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×#22626044
unambiguous semidirect productD73⋊#1949

Splittings

FittingC2×C4⋊C8×C73 ⋊ C4
SylowC73 ⋊ C2×#1949

Subgroups

subgroupG/H
centerC23C2×C4⋊#64408
commutatorC2×C4×C73C23×C4
FrattiniC2×C4C23×#64408
FittingC2×C4⋊C8×C73C4
socleC23×C73C2×C4⋊C4
prime radicalC23×D73C2×D4
cosocleC2×C4×D73C24
hypercenterC2×C4⋊C8#64408
hypocenterC73C2×#1949
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4⋊C8

1142 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4672

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 1105717);