Finite Group Databasebeta

C22×#16812632 #28371606

order13952
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC22×#16812632

Splittings

SylowC109 ⋊ C22×#107

Subgroups

subgroupG/H
centerC24C22⋊D109
commutatorC4×C109C23×C4
FrattiniC2×C4C23×D109
FittingC22×C4⋊C4×C109C2
socle, prime radicalC24×C109D4
cosocleC2×C4×C109C24
hypercenterC22×C4⋊C4D109
hypocenterC109C22×#107
LCSG ▷ C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×C4⋊C4

600 conjugacy classes of subgroups; only the 349 normal subgroups are shown.

normal subgroups only

This group has 600 conjugacy classes of subgroups — too many to draw. Only its 349 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) = 13952

Conjugacy classes & character table

2216 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 13084);