Finite Group Databasebeta

#107×Dic166 #35423243

order21248
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct product#107×Dic166

Splittings

SylowC83 ⋊ Q8×#107

Subgroups

subgroupG/H
centerC23C2×D4×D83
commutatorC2×C4×C83C23×C4
FrattiniC22×C4C23×D83
FittingC4×#107×C83C2
socle, prime radicalC23×C83C22×D4
cosocleC22×C4×C83C24
hypercenterC4×#107D83
hypocenterC83Q8×#107
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#107

838 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 21248

Conjugacy classes & character table

2366 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 188407);