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D21×D145 #27131802

order12180
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

direct productD21×D145

Splittings

Fitting, socle, derived, HallC3×C5×C7×C29 ⋊ C22
HallC5×C7×C29 ⋊ C2×D3
HallC3×C7×C29 ⋊ C2×D5
HallC3×C5×C29 ⋊ C2×D7
HallC7×C29 ⋊ D3×D5
HallC5×C29 ⋊ C2×D21
HallC3×C5×C7 ⋊ C2×D29
HallC3×C29 ⋊ D5×D7
HallC5×C7 ⋊ D3×D29
SylowC29 ⋊ D5×D21
HallC3×C7 ⋊ C2×D145
HallC3×C5 ⋊ D7×D29
SylowC7 ⋊ D3×D145
SylowC5 ⋊ D21×D29
SylowC3 ⋊ D7×D145

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC3×C5×C7×C29C22
LCSG ▷ C3×C5×C7×C29
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

888 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD63×D145, C3⋊AGL(1,𝔽7)×D145, C3×D21×D145, …
maximal normal subgroup ofC3⋊AGL(1,𝔽7)×D145, C3×D21×D145
maximal quotient ofD63×D145, C3×D21×D145, D21×D435, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12180, 137);