Finite Group Databasebeta

← Prev (#33238958) Next (#33238960) →

C22×C4⋊#11924003 #33238959

order18688
automorphism?
homologyAbelianization (H1) = C23×C16 · Schur multiplier (H2) = C26

Aliases

direct productC22×C4⋊#11924003

Splittings

SylowC73 ⋊ C22×C4⋊C16

Subgroups

subgroupG/H
centerC23×C8C2×D73
commutatorC2×C73C23×C16
FrattiniC2×C8C23×D73
FittingC22×C4×C8×C73C2
socle, prime radicalC24×C73C2×C8
cosocleC2×C8×C73C24
hypercenterC22×C4×C8D73
hypocenterC73C22×C4⋊C16
LCSG ▷ C2×C73 ▷ C73
UCSC1 ◁ C23×C8 ◁ C22×C4×C8

862 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18688

Conjugacy classes & character table

4768 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 322543);