Finite Group Databasebeta

#386×D167 #36326552

order21376
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C28

Aliases

direct product#386×D167

Splittings

Fitting#386×C167 ⋊ C2
SylowC167 ⋊ C2×#386

Subgroups

subgroupG/H
center, FrattiniC23C23×D167
commutatorC22×C167C23×C4
Fitting#386×C167C2
socle, cosocleC23×C167C24
prime radicalC22×D4×D167C2
hypercenter#386D167
hypocenterC167C2×#386
LCSG ▷ C22×C167 ▷ C167
UCSC1 ◁ C23 ◁ #386

1576 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5344

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, 6924);