Finite Group Databasebeta

#391×D167 #36326604

order21376
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4

Aliases

direct product#391×D167

Splittings

Fitting#391×C167 ⋊ C2
SylowC167 ⋊ C2×#391

Subgroups

subgroupG/H
center, FrattiniC23C23×D167
commutatorC22×C167C23×C4
Fitting#391×C167C2
socle, cosocleC23×C167C24
prime radicalC23×D167C23
hypercenter#391D167
hypocenterC167C2×#391
LCSG ▷ C22×C167 ▷ C167
UCSC1 ◁ C23 ◁ #391

928 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10688

Conjugacy classes & character table

2380 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21376, 6976);