Finite Group Databasebeta

C22×C22⋊(C107⋊C8) #28344893

order13696
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C27

Aliases

direct productC22×C22⋊(C107⋊C8)

Splittings

SylowC107 ⋊ C22×C22⋊C8

Subgroups

subgroupG/H
centerC23×C4C2×D107
commutatorC2×C107C23×C8
FrattiniC2×C4C23×D107
FittingC24×C4×C107C2
socleC24×C107C2×C4
prime radicalC25×C107C4
cosocleC2×C4×C107C24
hypercenterC24×C4D107
hypocenterC107C22×C22⋊C8
LCSG ▷ C2×C107 ▷ C107
UCSC1 ◁ C23×C4 ◁ C24×C4

1072 conjugacy classes of subgroups; only the 469 normal subgroups are shown.

normal subgroups only

This group has 1072 conjugacy classes of subgroups — too many to draw. Only its 469 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) = 6848

Conjugacy classes & character table

3472 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13696, 12942);