Finite Group Databasebeta

C22×#17988455 #33244262

order18688
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC22×#17988455

Splittings

SylowC73 ⋊ C22×#383

Subgroups

subgroupG/H
centerC25C22×D73
commutatorC22×C73C24×C4
FrattiniC23C24×D73
FittingC23×C42×C73C2
socle, prime radicalC25×C73C23
cosocleC23×C73C25
hypercenterC23×C42D73
hypocenterC73C22×#383
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C25 ◁ C23×C42

3678 conjugacy classes of subgroups; only the 1771 normal subgroups are shown.

normal subgroups only

This group has 3678 conjugacy classes of subgroups — too many to draw. Only its 1771 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18688

Conjugacy classes & character table

4720 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 327846);