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ΓL(1,𝔽8)×Dic445 #49153128

order37380
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

direct productΓL(1,𝔽8)×Dic445
unambiguous semidirect product(C7×Dic445)⋊C3

Splittings

derived, HallC5×C7×C89 ⋊ C3×C4
HallC7×Dic445 ⋊ C3
HallC5×ΓL(1,𝔽8)×C89 ⋊ C4
HallΓL(1,𝔽8)×C89 ⋊ Dic5
HallC7×C89 ⋊ C3×Dic5
HallC5×C89 ⋊ C4×ΓL(1,𝔽8)
HallC5×ΓL(1,𝔽8) ⋊ Dic89
SylowC89 ⋊ Dic5×ΓL(1,𝔽8)
HallC5×C7 ⋊ C3×Dic89
SylowC7 ⋊ C3×Dic445
SylowC5 ⋊ ΓL(1,𝔽8)×Dic89

Subgroups

subgroupG/H
center, Frattini, hypercenterC2ΓL(1,𝔽8)×D445
commutator, hypocenterC5×C7×C89C3×C4
Fitting, socle, cosocleC2×C5×C7×C89C2×C3
prime radicalC2×C5×ΓL(1,𝔽8)×C89C2
LCSG ▷ C5×C7×C89
UCSC1 ◁ C2

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12460

Conjugacy classes & character table

2240 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37380, 22);