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C2×D1505 #20258244

order6020
automorphismAut(G) order 3034080
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD3010
direct productC2×D1505
unambiguous semidirect product(C2×C5)⋊D301
unambiguous semidirect product(C2×C7)⋊D215
unambiguous semidirect product(C2×C43)⋊D35

Splittings

Fitting, socleC2×C5×C7×C43 ⋊ C2
derived, HallC5×C7×C43 ⋊ C22
HallC7×C43 ⋊ C2×D5
HallC5×C43 ⋊ C2×D7
SylowC43 ⋊ C2×D35
HallC5×C7 ⋊ C2×D43
SylowC7 ⋊ C2×D215
SylowC5 ⋊ C2×D301

Subgroups

subgroupG/H
center, hypercenterC2D1505
commutator, hypocenterC5×C7×C43C22
FrattiniC1G
Fitting, socleC2×C5×C7×C43C2
LCSG ▷ C5×C7×C43
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1508 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C5⋊#14268594, C2×C5⋊#14268593, C2×C5⋊(ΓL(1,𝔽8)⋊D43), …
maximal normal subgroup ofC2×C5⋊#14268594, C2×C5⋊#14268593, C2×C5⋊(ΓL(1,𝔽8)⋊D43), …
maximal quotient ofD3×D1505, C2×D4515, C2×C3×D1505, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6020, 32);