Finite Group Databasebeta

C23×#88102 #16808145

order3328
isoclinismisoclinic class of #88101
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC23×#88102
unambiguous semidirect productD13⋊(C22×#107)

Splittings

FittingC23×C8×C13 ⋊ C4
SylowC13 ⋊ C23×#107

Subgroups

subgroupG/H
centerC24C4⋊#261
commutatorC4×C13C24×C4
FrattiniC4C24×#261
FittingC23×C8×C13C4
socleC24×C13C4⋊C4
prime radicalC24×D13D4
cosocleC4×D13C25
hypercenterC23×C8#261
hypocenterC13C23×#107
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C24 ◁ C23×C4 ◁ C23×C8

3614 conjugacy classes of subgroups; only the 1464 normal subgroups are shown.

normal subgroups only

This group has 3614 conjugacy classes of subgroups — too many to draw. Only its 1464 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) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1114794);