Finite Group Databasebeta

C4×C22⋊C4×#64408 #34014573

order18688
automorphism?
homologyAbelianization (H1) = C2×C43 · Schur multiplier (H2) = C24×C43

Aliases

direct productC4×C22⋊C4×#64408

Splittings

FittingC4×C22⋊C4×C73 ⋊ C4
SylowC73 ⋊ C42×C22⋊C4

Subgroups

subgroupG/H
centerC22×C4C22×#64408
commutatorC2×C73C2×C43
FrattiniC23C23×#64408
FittingC4×C22⋊C4×C73C4
socleC23×C73C23×C4
prime radicalC24×D73C23
cosocleC23×D73C24
hypercenterC4×C22⋊C4#64408
hypocenterC73C42×C22⋊C4
LCSG ▷ C2×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ C4×C22⋊C4

3342 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2336

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 1098157);