Finite Group Databasebeta

← Prev (#44545075) Next (#44545077) →

C4×C17×C157⋊C3 #44545076

order32028
automorphism?
homologyAbelianization (H1) = C3×C4×C17 · Schur multiplier (H2) = C1

Aliases

direct productC4×C17×C157⋊C3
unambiguous semidirect product(C4×C157)⋊(C3×C17)
unambiguous semidirect product(C4×C17×C157)⋊C3

Splittings

Fitting, HallC4×C17×C157 ⋊ C3
derived, SylowC157 ⋊ C3×C4×C17
HallC17×C157 ⋊ C3×C4
HallC4×C157 ⋊ C3×C17

Subgroups

subgroupG/H
center, hypercenterC4×C17C157⋊C3
commutator, hypocenterC157C3×C4×C17
FrattiniC2C2×C17×C157⋊C3
FittingC4×C17×C157C3
socleC2×C17×C157C2×C3
prime radicalC2×C17×C157⋊C3C2
cosocleC2×C157C2×C3×C17
LCSG ▷ C157
UCSC1 ◁ C4×C17

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10676

Conjugacy classes & character table

3740 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32028, 2);