Finite Group Databasebeta

#108×D47 #15689167

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

Aliases

direct product#108×D47

Splittings

Fitting#108×C47 ⋊ C2
SylowC47 ⋊ C2×#108

Subgroups

subgroupG/H
centerC4D4×D47
commutatorC4×C47C22×C4
FrattiniC2×C4C22×D47
Fitting#108×C47C2
socleC2×C47C2×C4⋊C4
prime radicalC22×D47Q8
cosocleC2×C4×C47C23
hypercenter#108D47
hypocenterC47C2×#108
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C2×C4 ◁ #108

106 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 752

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, 593);