Finite Group Databasebeta

← Prev (#34068973) Next (#34068975) →

C4⋊C4×C151⋊C8 #34068974

order19328
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4

Aliases

direct productC4⋊C4×C151⋊C8

Splittings

SylowC151 ⋊ C8×C4⋊C4

Subgroups

subgroupG/H
center, FrattiniC22×C4C22×D151
commutatorC2×C151C2×C4×C8
FittingC4×C4⋊C4×C151C2
socle, prime radicalC23×C151C22×C4
cosocleC22×C4×C151C23
hypercenterC4×C4⋊C4D151
hypocenterC151C8×C4⋊C4
LCSG ▷ C2×C151 ▷ C151
UCSC1 ◁ C22×C4 ◁ C4×C4⋊C4

296 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 181 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) = 19328

Conjugacy classes & character table

3080 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19328, 4374);