Finite Group Databasebeta

C23×#6399 #14217383

order1792
isoclinismisoclinic class of #1141
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC23×#6399

Splittings

FittingC23×C7×M16 ⋊ C2
SylowC7 ⋊ C23×#104

Subgroups

subgroupG/H
centerC23×C4C22⋊D7
commutatorC4×C7C24×C4
FrattiniC2×C4C24×D7
FittingC23×C7×M16C2
socleC24×C7C22⋊C4
prime radicalC23×#1157C2
cosocleC2×C4×C7C25
hypercenterC23×M16D7
hypocenterC7C23×#104
LCSG ▷ C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23×C4 ◁ C24×C4 ◁ C23×M16

5758 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 448

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 1033155);