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ΓL(1,𝔽8)×Dic403 #46799265

order33852
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

direct productΓL(1,𝔽8)×Dic403

Splittings

derived, HallC7×C13×C31 ⋊ C3×C4
HallC7×Dic403 ⋊ C3
HallC13×ΓL(1,𝔽8)×C31 ⋊ C4
HallΓL(1,𝔽8)×C31 ⋊ Dic13
HallC13×C31 ⋊ C4×ΓL(1,𝔽8)
HallC13×ΓL(1,𝔽8) ⋊ Dic31
HallC7×C31 ⋊ C3×Dic13
HallC7×C13 ⋊ C3×Dic31
SylowC31 ⋊ ΓL(1,𝔽8)×Dic13
SylowC13 ⋊ ΓL(1,𝔽8)×Dic31
SylowC7 ⋊ C3×Dic403

Subgroups

subgroupG/H
center, Frattini, hypercenterC2ΓL(1,𝔽8)×D403
commutator, hypocenterC7×C13×C31C3×C4
Fitting, socle, cosocleC2×C7×C13×C31C2×C3
prime radicalC2×C13×ΓL(1,𝔽8)×C31C2
LCSG ▷ C7×C13×C31
UCSC1 ◁ C2

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11284

Conjugacy classes & character table

2030 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33852, 60);