Finite Group Databasebeta

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C17×Dic157⋊C3 #44545084

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

Aliases

direct productC17×Dic157⋊C3
unambiguous semidirect productDic157⋊(C3×C17)
unambiguous semidirect product(C17×Dic157)⋊C3

Splittings

derived, SylowC157 ⋊ C3×C4×C17
HallC17×Dic157 ⋊ C3
HallC17×C157⋊C3 ⋊ C4
HallC17×C157 ⋊ C3×C4
HallDic157 ⋊ C3×C17
HallC157⋊C3 ⋊ C4×C17

Subgroups

subgroupG/H
center, hypercenterC2×C17D157⋊C3
commutator, hypocenterC157C3×C4×C17
FrattiniC2C17×D157⋊C3
Fitting, socleC2×C17×C157C2×C3
prime radicalC2×C17×C157⋊C3C2
cosocleC2×C157C2×C3×C17
LCSG ▷ C157
UCSC1 ◁ C2×C17

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10676

Conjugacy classes & character table

1088 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32028, 10);