Finite Group Databasebeta

← Prev (#37550702) Next (#37550704) →

2−1+4×#10624382 #37550703

order23168
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct product2−1+4×#10624382

Splittings

Fitting2−1+4×C181 ⋊ C4
SylowC181 ⋊ C4×2−1+4

Subgroups

subgroupG/H
center, FrattiniC2C24×#10624382
commutator, socleC2×C181C24×C4
Fitting2−1+4×C181C4
prime radical2−1+4×D181C2
cosocleC2×D181C25
hypercenter2−1+4#10624382
hypocenterC181C4×2−1+4
LCSG ▷ C2×C181 ▷ C181
UCSC1 ◁ C2 ◁ 2−1+4

1492 conjugacy classes of subgroups; only the 754 normal subgroups are shown.

normal subgroups only

This group has 1492 conjugacy classes of subgroups — too many to draw. Only its 754 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) = 2896

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23168, 21492);