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#261×#3861 #21439655

order7644
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

direct product#261×#3861

Splittings

Fitting, socle, derived, HallC72×C13 ⋊ C3×C4
HallC72×#261 ⋊ C3
HallC13×#3861 ⋊ C4
SylowC72 ⋊ C3×#261
SylowC13 ⋊ C4×#3861

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC72×C13C3×C4
LCSG ▷ C72×C13
UCSC1

120 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

133 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#37524883, ΓL(1,𝔽8)2×#261, #3861×AGL(1,𝔽13), …
maximal normal subgroup of#37524883, ΓL(1,𝔽8)2×#261, #3861×AGL(1,𝔽13), …
maximal quotient of#261×#89204, C3×#261×#3861, #3861×C3⋊#261, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7644, 224);