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C3×C17×Dic49 #23756104

order9996
isoclinismisoclinic class of D49
automorphism?
homologyAbelianization (H1) = C3×C4×C17 · Schur multiplier (H2) = C1

Aliases

direct productC3×C17×Dic49

Splittings

derived, SylowC49 ⋊ C3×C4×C17
HallC3×C17×C49 ⋊ C4
HallC17×C49 ⋊ C3×C4
HallC3×C49 ⋊ C4×C17

Subgroups

subgroupG/H
center, hypercenterC2×C3×C17D49
commutator, hypocenterC49C3×C4×C17
FrattiniC2×C7C3×D7×C17
FittingC2×C3×C17×C49C2
socle, prime radicalC2×C3×C7×C17D7
cosocleC2×C49C2×C3×C17
LCSG ▷ C49
UCSC1 ◁ C2×C3×C17

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2652 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC17×Dic49⋊C9, C9×C17×Dic49, C3×C17×(C49⋊C3)⋊C4, …
maximal normal subgroup ofC17×Dic49⋊C9, C9×C17×Dic49, C3×C17×(C49⋊C3)⋊C4, …
maximal quotient ofC9×C17×Dic49, C32×C17×Dic49, C3×C17×Dic147

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9996, 7);