Finite Group Databasebeta

#107×D47 #15689155

order3008
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct product#107×D47

Splittings

Fitting#107×C47 ⋊ C2
SylowC47 ⋊ C2×#107

Subgroups

subgroupG/H
centerC22D4×D47
commutatorC4×C47C22×C4
FrattiniC2×C4C22×D47
Fitting#107×C47C2
socleC22×C47C2×D4
prime radicalC22×D47D4
cosocleC2×C4×C47C23
hypercenter#107D47
hypocenterC47C2×#107
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

130 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1504

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3008, 581);